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Boolean approach to planar embeddings of a graph. (English) Zbl 0780.05017
Summary: The purpose of this paper, which is a sequel of our paper [ibid., New Ser. 4, No. 4, 316-326 (1988; Zbl 0671.05031)], is to show the following results.
(1) Both of the problems of testing the planarity of graphs and embedding a planar graph into the plane are equivalent to finding a spanning tree in another graph whose order and size are bounded by a linear function of the order and the size of the original graph, respectively.
(2) The number of topologically non-equivalent planar embeddings of a Hamiltonian planar graph \(G\) is \(\tau(G)=2^{c(H)-1}\), where \(c(H)\) is the number of components of the graph \(H\) which is related to \(G\).

MSC:
05C10 Planar graphs; geometric and topological aspects of graph theory
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References:
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